The minimum measurable eccentricity from gravitational waves of LISA massive black hole binaries
arXiv (Cornell University)(2023)
摘要
We explore the eccentricity measurement threshold of LISA for gravitational
waves radiated by massive black hole binaries (MBHBs) with redshifted BH masses
M_z in the range 10^4.5-10^7.5 M_⊙ at redshift z=1. The
eccentricity can be an important tracer of the environment where MBHBs evolve
to reach the merger phase. To consider LISA's motion and apply the time delay
interferometry, we employ the lisabeta software and produce year-long eccentric
waveforms using the inspiral-only post-Newtonian model TaylorF2Ecc. We study
the minimum measurable eccentricity (e_ min, defined one year before the
merger) analytically by computing matches and Fisher matrices, and numerically
via Bayesian inference by varying both intrinsic and extrinsic parameters. We
find that e_ min strongly depends on M_z and weakly on mass ratio and
extrinsic parameters. Match-based signal-to-noise ratio criterion suggest that
LISA will be able to detect e_ min∼10^-2.5 for lighter systems
(M_z≲10^5.5 M_⊙) and ∼10^-1.5 for heavier MBHBs
with a 90 per cent confidence. Bayesian inference with Fisher initialization
and a zero noise realization pushes this limit to e_ min∼10^-2.75
for lower-mass binaries, assuming a <50 per cent relative error. Bayesian
inference can recover injected eccentricities of 0.1 and 10^-2.75 for a
10^5 M_⊙ system with a ∼10^-2 per cent and a ∼10 per
cent relative errors, respectively. Stringent Bayesian odds criterion
(lnB>8) provides nearly the same inference. Both analytical and numerical
methodologies provide almost consistent results for our systems of interest.
LISA will launch in a decade, making this study valuable and timely for
unlocking the mysteries of the MBHB evolution.
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关键词
gravitational waves,massive black hole binaries,minimum measurable eccentricity,lisa
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